Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 80, pp. 1-14.
Title: Controllability of matrix second order systems:
A trigonometric matrix approach
Authors: Jaita Pankaj Sharma (Univ. of Baroda, Vadodara, India)
Raju K. George (Univ. of Baroda, Vadodara, India)
Abstract:
Many of the real life problems are modelled as Matrix Second Order
Systems, (refer Wu and Duan [19], Hughes and
Skelton [10]). Necessary and sufficient condition for
controllability of Matrix Second Order Linear (MSOL) Systems has
been established by Hughes and Skelton [10]. However, no
scheme for computation of control was proposed. In this paper we
first obtain another necessary and sufficient condition for the
controllability of MSOL and provide a computational algorithm for
the actual computation of steering control. We also consider a
class of Matrix Second Order Nonlinear systems (MSON) and provide
sufficient conditions for its controllability. In our analysis we
make use of Sine and Cosine matrices and employ Pade
approximation for the computation of matrix Sine and Cosine. We
also invoke tools of nonlinear analysis like fixed point theorem
to obtain controllability result for the nonlinear system. We
provide numerical example to substantiate our results.
Submitted February 15, 2007. Published May 29, 2007.
Math Subject Classifications: 93B05, 93C10.
Key Words: Controllability; matrix second order linear system;
cosine and sine matrices; Banach contraction principle.